Question

How do you graph \[3x - 4y = - 18\] by plotting points?

Answer 1

Hint: To graph an equation by plotting points, we must find x and y intercepts. The x-intercepts are the points at which the graph crosses the x-axis. To find the x-intercept, set y = 0 and solve for x, to find the y-intercept, set x = 0 and solve for y, hence we get the x and y intercepts by solving and to graph a line, graph the points if they exist, and then connect the two points with a straight line.

Complete step by step solution:
 Let us write the given linear equation:
 \[3x - 4y = - 18\]
To graph the solution for the given equation, we need to find x and y intercepts.
Let us find the x-intercepts: To find the x-intercept, set y = 0 and solve for x i.e.,
\[3x - 4y = - 18\]
\[3x - 4\left( 0 \right) = - 18\]
\[3x = - 18\]
Divide both sides of the equation by 3 to get the value of x as
\[\dfrac{{3x}}{3} = - \dfrac{{18}}{3}\]
\[ \Rightarrow \]\[x = - \dfrac{{18}}{3}\]
We get the value of x as,
\[x = - 6\]
Hence, the x-intercept of the given equation is \[\left( { - 6,0} \right)\].
Now let us find the y-intercepts: To find the y-intercept, set x = 0 and solve for y i.e.,
\[3x - 4y = - 18\]
\[3\left( 0 \right) - 4y = - 18\]
\[ - 4y = - 18\]
Divide both sides of the equation by 4 to get the value of y as
\[\dfrac{{ - 4y}}{4} = - \dfrac{{18}}{4}\]
\[ \Rightarrow \]\[y = \dfrac{{18}}{4}\]
The value of y is,
\[ \Rightarrow \]\[y = \dfrac{9}{2}\]
Hence, the y-intercept of the given equation is \[\left( {0,\dfrac{9}{2}} \right)\] or \[\left( {0,4.5} \right)\]
Now, let us graph the solution: To graph this line using the intercepts, first graph the two points as shown A =\[\left( {0,4.5} \right)\] and B = \[\left( { - 6,0} \right)\], then connect the two points with a straight line.

Note: The key point the plot the points is that the ordered pair is very important, in which x-intercept is found by the value of x when y = 0, \[\left( {x,0} \right)\] and y-intercept is found by the value of y when x = 0, \[\left( {0,y} \right)\]and when we are finding x-intercept y-coordinate is zero and vice versa then solve for x and y intercepts and the line can be graphed using two points.